• # Coherent Source problem from class 11

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S1 and S2 are two coherent sources of radiations separated by distance 100.25 , where the wave length of radiation. S1 leads S2 in phase by pi/2. A and B are two points on the line joining S1 and S2. The ratio of amplitudes of component waves from source S1 and S2 at A and B are in ratio 1:2. The ratio of intensity at A to that of B Ia/Ib is:?

• Let wavelength be = X
For interference at A : S2 is behind of S1 by a distance of 100 X+
X/4.(equal to phase difference Pi/2 ).
Further S2 lags S1 by Pi/2. Hence the waves from S1 and S2 interfere at A with a phase difference of
$200.5 \pi+ 0.5\pi$
= 201pi
=pi
Hence the net amplitude at A is 2a – a = a
For interference at B : S2 is ahead of S1 by a distance of 100X + X/4.(equal to phase difference pi/2 ).
Further S2 lags S1 by pi/2.
Hence waves from S1 and S2 interfere at B with a phase difference of
200.5pi – 0.5po = 200pi = 0pi .
Hence the net amplitude at A is 2a + a = 3a
Hence
Ia/ Ib= (a/3a)^2= 1/9 Ans.

Saket Kumar
Real Eyes Realize Real Lies.